Dimensionality reflects distinct natures or independent degrees of freedom of a single particle, a many-body physical system or an object. The concept of dimensionality is very general and wide and could even not be limited to conventional physical systems, e.g., the dimensionality of (animal) behavior could be defined as the minimum number of features of the past needed to make the maximally informative predictions about the future [1]}. Fundamentally, the spatial dimension of a physical system is normally defined as the minimum number of coordinates needed to specify any point within it.
Since ordinary lifes and conventional physical systems live in three dimensions, their spatial degree of freedom are often frozen to three. It does not, however, mean that the problem in other dimensions is unimportant or irrelevant. In fact, it really helped in history to develop modern physical methodologies or improve the understanding on certain types of important theoretical issues, by considering the spatial dimension \(d\)  as a continuous or a discrete variable. For example, the dimension regularization technique in quantum field theories [2]} writing a Feynman integral as an integral depending on the space-time dimension \(d+1\)  instead of four solved for the first time the divergence problem of the gauge fields [3]}.
On the other hand, the exact solution of the two-dimensional squared Ising model by L. Onsager [4]} not only provided deep insight into the phase transition problems [5]} but also largely prompted the development of modern statistical physics, such as the low- and high- temperature expansions, the critical phenomena and the renormalization group, see, e.g., Ref. [6]} for a modern introduction on these issues.
The last three to four decades actually have witnessed many exciting novel features as well as important breakthroughs in systems with reduced dimensions, such as the 2-dimensional electron gas [7]}, the graphene [8]}, and the topological insulator [9]}, [10]}.
One of the crucial characteristics of these 2-dimensional systems is the constant density of state which is independent of energy or momentum [11]}, and it is this feature (partially) makes the 2D systems novel and peculiar.
